Offset error in linear feedback loops corrected by loop replication

ABSTRACT

A system of connecting errors in the control loop using multiple additional loops. A first loop carries out control in a desired way, and the additional loops are provided for the purpose of determining a specified error value. That specified error value may be, for example, a quiescent current. The specified error value is then used to correct for errors in the first loop.

BACKGROUND

Control of a functional unit may be carried out using a control system.A linear feedback control loop may be used to generate such a signal.Linear feedback loops may be used in various kinds of control, includingmotors, pumps and electronic components.

The precision of the input signal to a linear feedback control loop maybe determined from the open loop gain of the system. Differenttechnological issues may affect the gain and precision of such a controlloop.

For example, such loops may have an offset error. The offset error maybe reduced by increasing the gain of the loop. A loop with infinite gainmight have zero offset error. However, the gain of each real lifecomponent is subject to physical limitations. This often requires thatadditional amplifying elements be used within the loop. These amplifyingelements may undesirably increase phase delay through the loop. Thebandwidth of the loop may need to be reduced in order to slow theresponse of the system.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects will now be described in detail with referenceto the accompanying drawings, wherein:

FIG. 1 shows a basic block diagram of an electrical control loop; and

FIG. 2 shows a basic block diagram of the control loop in more genericformat; and

FIG. 3 shows a 2 loop version of the present system which correctsoffset errors in a control loop;

FIG. 4 shows and n loop version of the control loop;

FIG. 5 shows a transistor level schematic of the 2 loop version; and

FIG. 6 shows a transistor level diagram of the basic control loopstructure.

DETAILED DESCRIPTION

An embodiment may stabilize control loops. The prior art has oftenincreased a gain within a control loop in order to decrease the offseterror, as described above. In contrast, the present system uses aplurality of basic loops which are connected together to decrease theoffset error. Each of these loops may have a lower gain than a singleloop would have, in order to provide comparable offset error.

A first loop in the sequence may operate similar to the conventionalloop. Each successive loop in the sequence of loops may use informationfrom the previous loops in order to displace offset, and bring theoffset as close to zero as possible. As disclosed herein, if n loops areused, each loop having an open loop gain of T, then the offset in thenth loop may be approximately 1/T^(n) times that of a single loop.

This system may allow offset error to be reduced without significantlychanging the stability of the system, or slowing the system, and hencewithout significantly reducing the bandwidth of the system.

This system may therefore be used with any of a number of differentlinear feedback control systems as described herein. The example givenherein explains the operation for the embodiment of an electricalcircuit implementation. However, other implementations may also be used.

A standard control loop for a differential amplifier is shown in FIG. 1.Element 100, labeled as B(•) represents the item to be controlled. Theoutput from the item to be controlled 100 is labeled as V_(f)=B(V_(c)).This value is fed back to the feedback input 112 of the amplifier 110.

The amplifier 110 is a differential amplifier, driven by an input signalV_(r) and by the feedback signal V_(f) in a conventional way, e.g., as adifferential amplifier.

For a well-designed amplifier that operates within a specific range, theamplifier output may be approximated as

V _(c) =V _(o) +G(V _(r) −V _(f)),  (1)

where G is the differential amplifier gain, and V_(o) is the quiescentoutput voltage.

FIG. 2 shows a similar basic control loop rewritten in a more genericsignal flow graph. This signal flow graph is applicable to bothelectrical and nonelectrical signals. The system in FIG. 2 includes afirst object 200 receiving the feedback and the driving signal, a secondobject 210, receiving the signal S_(o), and the driven object 100. Thesystem of FIG. 2 may be defined in terms of the equationss_(c)=s_(o)+G(s_(r)−s_(f)) and s_(f)=B(s_(c)). In an ideal system withinfinite gain, the loop would produce the control signals_(c)=B⁻¹(s_(r)), which is effectively the signal that forces thereference and feedback signals to become equal. However, when G isfinite, as it will be in every real system, the solution will deviatefrom this ideal case. The deviation is quantified by the “input offseterror”

e _(i) =s _(f) −s _(r)  (2),

that is the difference between the feedback signal and the input signal.

This input offset error can be calculated.

First, the static transfer characteristics of the unit under control areapproximated by

s _(f) =B(s _(c))@B(s _(o))+G _(B)(s _(c) −s _(o))  (3),

where G_(B)=[dB(x)/dx]_(x=s) _(o) is the small-signal gain of the unitunder control.

The offset error can then be calculated as

e _(i)=(B(s _(o))−s _(r))/(1+G _(B) G).  (4)

As the equation 4 shows, the offset error originates in the discrepancybetween the quiescent output, s_(o), and the desired control signal,B⁻¹(s_(r)). Limited a priori knowledge of s_(r), s_(o), and B( ),however, may restrict a designers ability to control the offset error.

The conventional approach to reducing e_(i) has thus been to increase G,thereby increasing the denominator in equation (4) and reducing e_(i).However, any given kind of amplifier has a limited gain. Since the gainof a single amplifier stage is limited, the overall gain has typicallybeen increased by cascading multiple stages. In order to maintain thestability of the system, therefore, bandwidth of the system may berestricted. This may increase the response time of the system and may beunacceptable in certain applications.

The present application may reduce this offset in a new way by addingadditional control loops instead of by increasing the system gain. Eachadditional control loop may reduce the error. For example, the error maybe reduced by a factor related to a gain factor of the loop raised tothe number of additional control loops beyond the basic loop.

The embodiment of FIG. 3 shows a 2 loop version of the system, with loop#1 labeled as element 310, and loop #2 labeled as element 320. Inoperation, loop #1 operates to calculate a correction factor which isapplied to loop #2.

The differential amplifier 110 is replaced in the two loopimplementation by a more complex differential amplifier. The amplifier300 in loop No. 1 is a differential amplifier 302 with a first input 304having a gain G1 and a second input 306 having a gain G2. In the firstloop, the second input has its values tied together and connected to theinput signal S_(r). The second input pair 304 includes a first valuetied to S_(r), and a second value receiving the feedback output of thedriven device B(.).

Note that loop No. 1 therefore becomes functionally similar to thesystem in FIG. 1. As such, it has the same error as in FIG. 1, that isit operates with an input offset error

e _(i1)=(B(s _(o))−S _(r))/(1+G _(B) G ₁).

Similar components are present in the second loop 320, and this errorfrom the first loop is used to correct the error in the second loop andthereby provide a corrected output.

The second loop 320, loop #2, includes a similar amplifier shown as 330.This amplifier includes the same gains G₁ and G₂, but has its inputsconfigured slightly differently. The loops could be the same, or similarbut “scaled”. The inputs to the first differential pair 332 in loop No.2 include the input value S_(r) and the feedback value S_(fb). Hence,the difference between the inputs to the first differential pair ise_(i1).

Thus, the output of loop #2 amplifier is

s _(c2) =s _(o) −G ₁ e _(i1) +G ₂(s _(r) −s _(f2)).

This is analogous to the single loop, but with an effective quiescentoutput signal of

s _(o2) =s _(o) −G ₁ e _(i1).

Loop #1, then, is effectively being used to calculate a correction tothis quiescent output. The quiescent output of loop #2 is displaced bythis amount, based on the positive input to differential pair 334, toreduce the offset error.

Assuming that the derivative of B( ) is evaluated and s_(o) and s_(o2)are approximately equal to the same value G_(B), the offset error forloop #2 can be considered as

e _(i2)=(B(s _(o))−s _(r))/[(1+G _(B) G ₁)(1+G _(B) G ₂)].

This compares with the single loop case given above, where the offseterror is:

e _(i)=(B(s _(o))−s _(r))/(1+G _(BG).)

Taking all the gains being the same, this becomes equivalent toincreasing the gain in the basic loop by a factor of approximatelyG_(B)G. This is done without increasing the loop order, however, andtherefore the dynamics, and specifically, the bandwidth of the systemare not affected. Because of this use of second order loops, the overallsystem can run as fast as the corresponding second order loop; that is,the bandwidth of the original loop is only minimally affected.

The above has described the situation of the two-loop system. Evenfurther decreases the may be obtained by adding additional loops. FIG. 4shows a system with n loops. In this n-loop system, each amplifier suchas 400 has n differential inputs. Also, in this n-loop system, the inputoffset error of the n^(th) loop is given by

e _(in)=(B(s _(o))−s _(r))/(1+G _(B) G)^(n).

The offset error in this n loop case is decreased by the gain G_(B)Graised to the power of the number of loops. In this n-loop system,therefore, the offset error can be made arbitrarily small withoutincreasing G or sacrificing the bandwidth.

FIG. 5 shows a transistor level schematic of the two loop version,implemented in the P858 process. The original circuit of this type,shown in FIG. 6, had an offset error of 4 mv. The FIG. 5 circuitachieves a much lower offset error of 0.3 millivolts: a 13-fold errorreduction. Both the original circuit and the new circuit have the samesettling time of 6 ns, emphasizing that the bandwidth of the system isnot compromised.

What is claimed is:
 1. A control system, comprising; a first loop,including a first amplifying element, said first amplifying elementproducing an output signal based on first and second inputs thereto, andhaving an output forming a feedback loop to one of said inputs; and asecond loop, including a second amplifying element therein, said secondloop connected to produce a correction factor for said first loop, saidcorrection factor being connected to said first loop; and additionalloops, each of said n additional loops connected to apply respectivecorrection factors to said first loop.
 2. A control system, comprising;a first loop, including a first amplifying element, said firstamplifying element producing an output signal based on first and secondinputs thereto, and having an output forming a feedback loop to one ofsaid inputs; and a second loop, including a second amplifying elementtherein, said second loop connected to produce a correction factor forsaid first loop, said correction factor being connected to said firstloop, wherein said second amplifying element includes first and secondinputs with a first gain, and third and fourth inputs with a secondgain.
 3. A system as in claim 2, wherein said third and fourth inputsare connected to receive an input signal, said second input is connectedto receive said input signal, and said first input is connected toreceive a feedback signal.
 4. A system as in claim 3, wherein saidfeedback signal forms said correction factor for said first loop.
 5. Asystem as in claim 4, wherein said first amplifying element includesfirst and second inputs with a first gain, which is the same as saidfirst gain of said second amplifying element, and third and fourthinputs with a second gain, which is the same as said second gain of saidsecond amplifying element.
 6. A system as in claim 5, wherein saidfeedback signal is connected as said correction factor to said firstinput, and said input signal is connected to said second and fourthinputs, and a feedback signal within said first loop is connected tosaid third input.
 7. A method, comprising: carrying out a controloperation using a first loop with an amplifier operating to control adriven object, and to receive a feedback control from the driven objectindicative of an error in an amount of control; and using a second loop,with another amplifier to produce a correction factor for said firstloop and said first amplifier; and using n additional loops beside saidsecond loop to produce additional correction factors.
 8. A method as inclaim 7, wherein said each of said n additional loops each have anamplifier which is substantially similar to said amplifier in said firstloop.
 9. A method as in claim 8, wherein said second loop produces acorrection factor according to a gain of said amplifier raised to apower of a number of correcting loops.
 10. A method, comprising:carrying out a Control operation using a first loop with an amplifieroperating to control a driven object, and to receive a feedback controlfrom the driven object indicative of an error in an amount of control;and using a second loop, with another amplifier to produce a correctionfactor for said first loop and said first amplifier wherein said anotheramplifier in said second loop is substantially similar to said amplifierin said first loop, wherein each of said amplifier and said anotheramplifier include two gains G1 and G2, and wherein said correctionfactor reduces an error in said first loop by amount proportional to oneof said gains.